A negationless interpretation of intuitionistic theories

Erkenntnis 53 (1-2):155-179 (2000)
Abstract
In a seriesof papers beginning in 1944, the Dutch mathematician and philosopherGeorge Francois Cornelis Griss proposed that constructivemathematics should be developedwithout the use of the intuitionistic negation1 and,moreover, without any use of a nullpredicate.In the present work, we give formalized versions of intuitionisticarithmetic, analysis,and higher-order arithmetic in the spirit ofGriss' ``negationless intuitionistic mathematics''and then consider their relation to thecurrent formalizations of thesetheories
Keywords intuitionism  negationless intuitionistic mathematics  arithmetic  analysis  translatability
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DOI 10.1023/A:1005207512630
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